Question: Multiply the following complex numbers: $({-1-i}) \cdot ({-4+3i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-i}) \cdot ({-4+3i}) = $ $ ({-1} \cdot {-4}) + ({-1} \cdot {3}i) + ({-1}i \cdot {-4}) + ({-1}i \cdot {3}i) $ Then simplify the terms: $ (4) + (-3i) + (4i) + (-3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (-3 + 4)i - 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (-3 + 4)i - (-3) $ The result is simplified: $ (4 + 3) + (1i) = 7+i $